Solve for $x$ and $y$ using substitution. ${-3x+6y = 9}$ ${y = -5x+7}$
Solution: Since $y$ has already been solved for, substitute $-5x+7$ for $y$ in the first equation. ${-3x + 6}{(-5x+7)}{= 9}$ Simplify and solve for $x$ $-3x-30x + 42 = 9$ $-33x+42 = 9$ $-33x+42{-42} = 9{-42}$ $-33x = -33$ $\dfrac{-33x}{{-33}} = \dfrac{-33}{{-33}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {y = -5x+7}\thinspace$ to find $y$ ${y = -5}{(1)}{ + 7}$ $y = -5 + 7$ $y = 2$ You can also plug ${x = 1}$ into $\thinspace {-3x+6y = 9}\thinspace$ and get the same answer for $y$ : ${-3}{(1)}{ + 6y = 9}$ ${y = 2}$